Using the example of a second-order nonlinear system under the influence of consistent and inconsistent uncontrolled disturbances within the framework of the block approach, the problem of stabilization of the output variable in the presence of constraints on the state variables and control is considered. The first proposed approach with dynamic feedback in the form of nested saturators and compensation of disturbances, based on their estimates obtained using a second-order disturbance observer, provides almost exact linearization by feedback and asymptotic stabilization of the output. The second approach, simpler in computational implementation, with static feedback in the form of nested sigmoids, which are functions of the hyperbolic tangent, suppresses disturbances and provides stabilization of the output with some accuracy. An algorithm for adjusting the variable gain has been developed, which reduces the stabilization error without violating the specified constraints. The results of numerical modeling of the developed algorithms for the angular position control system of a single-link manipulator are presented.